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Macaulay2Doc :: fromDual

fromDual -- ideal from inverse system

Synopsis

Description

For other examples, and a more precise definition, see inverse systems.
i1 : R = ZZ/32003[x_1..x_3];
i2 : g = random(R^1, R^{-4})

o2 = | 7056x_1^4+2032x_1^3x_2+4642x_1^2x_2^2-13397x_1x_2^3+8757x_2^4-3166x_1^
     ------------------------------------------------------------------------
     3x_3-6209x_1^2x_2x_3-10313x_1x_2^2x_3-6800x_2^3x_3-5509x_1^2x_3^2+984x_
     ------------------------------------------------------------------------
     1x_2x_3^2+14275x_2^2x_3^2-15538x_1x_3^3-12964x_2x_3^3+3496x_3^4 |

             1       1
o2 : Matrix R  <--- R
i3 : f = fromDual g

o3 = | x_2^2x_3+14276x_1x_3^2-4453x_2x_3^2+14756x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+8634x_1x_3^2+6098x_2x_3^2+10492x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+2397x_1x_3^2+6917x_2x_3^2+14399x_3^3
     ------------------------------------------------------------------------
     x_2^3-4081x_1x_3^2-7106x_2x_3^2-6497x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-2985x_1x_3^2+3561x_2x_3^2-7904x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-9249x_1x_3^2-9502x_2x_3^2+13324x_3^3
     ------------------------------------------------------------------------
     x_1^3+3485x_1x_3^2-11826x_2x_3^2+9791x_3^3 |

             1       7
o3 : Matrix R  <--- R
i4 : res ideal f

      1      7      7      1
o4 = R  <-- R  <-- R  <-- R  <-- 0
                                  
     0      1      2      3      4

o4 : ChainComplex
i5 : betti oo

            0 1 2 3
o5 = total: 1 7 7 1
         0: 1 . . .
         1: . . . .
         2: . 7 7 .
         3: . . . .
         4: . . . 1

o5 : BettiTally

See also

Ways to use fromDual :